The binomial theorem shows a generalized way to expand the sum of two variables raised to some power . The general form of the binomial theorem is shown below.
Shown below is the binomial expansion for the first four cases of the binomial theorem, where is given by the combination formula for choosing elements from a set of elements.
| Case | Expression | Binomial Expansion |
|---|---|---|
The binomial theorem is closely related to Pascal’s Triangle, where each row of the triangle corresponds to the coefficients of the binomial expansion for a given power of .